# The Six Functions of Iinterest

**TIME VALUE OF MONEY**

Capitalization has been defined as the conversion of income to value. Value has been defined as the present worth of future benefits. The link or bridge that ties income to value and present to future is interest. Interest may be viewed as the price of time. The time at which one receives income or other benefits is critical to the value of the income or benefits.

Like the expression “A bird in the hand is worth two in the bush”, which deals with the time-value of birds, the expression “A dollar today is worth more than a dollar tomorrow, or a year from now” deals with the time-value of money or capital. In other words, sooner is more valuable than later, because the sooner one has money or capital, the sooner it may be reinvested to earn a return on the amount invested. Hence, the rate of interest is the return “on” investment as opposed to the return “of” investment or the capital recovery rate.

The interest rate is synonymous with the risk rate or the discount rate (which is the rate of interest or rate of return necessary to attract investment capital or to compensate the investor for the risks inherent in an investment). Finally, remember that the capitalization rate is the sum of the discount rate or the return “on” investment and the capital recovery rate or the return “of” investment.

**DEVELOPMENT OF THE THEORY**

The so-called six functions of the dollar or the six functions of interest comprise the mathematical formulations for dealing with time value of money as determined by the rate of interest. Although Henry William Inwood traditionally has been attributed with the development of these formulations, recent research has revealed this not to be the case. Inwood’s book, that now carries the title Inwood’s Tables of Interest and Mortality for the Purchasing of Estate and Valuation of Properties, was first published in1811 in England. However, another Englishman, Dr John Newton, published Ephemerides of Interest and Rate of Money at 6 Per Cent and The Scale of Interest in1667 and 1668, respectively. The second of these dealt primarily with the rates of interest charged and the present values of future leases of church property. No matter whether Inwood or Newton or someone before Newton was the first to derive the mathematical theorems and formulae for the six functions of interest, it is important to note that the mathematics per se is not appraising. The “number crunching” is merely a mechanical process used as an appraisal tool. Without good market data and the appraiser’s experience and judgment, the arithmetic manipulation of numbers is sterile and meaningless. Like with a computer, the old expression “garbage in – garbage out” applies here as well.

**TERMINOLOGY SEMANTICS**

Before a complete explanation of the six function of interest is presented, it is necessary to present and agree upon some common terminology. Terminology is almost never common across all fields of study. Hence, an attempt will be made here to minimize the number of terms employed in the explanation of the six functions of interest. One could argue that to use terms not commonly used elsewhere only adds to the terminology problem. However, it is hoped that the terms used here, although somewhat unique, may apply universally across all disciplines. Furthermore, by using only two basic terms, as opposed to many more that two, it is hoped that the relationship that exist among the six functions of interest will be much more readily apparent.

The two basic terms are “cash-flow” and “reversion”. A cash-flow is a periodic amount of money. A reversion is a single amount of money. Each of the two amounts of money may be stated in terms of the future or the present. Also, given either a future or present value of a series of cash-flows one might seek the amount of the cash-flow itself that is associated with the future or present value amount of the series of periodic cash-flows.

One might make payment of or take receipt of a cash-flow. In either case the cash-flow is periodic. The only difference between the two possibilities is the direction of the cash-flow or the point of reference for evaluating the cash-flow. For example, the borrower’s debt service to pay-off the present value of a loan is also the lender’s cash flow: and sinking fund payments made to accumulate to a future value are also cash-flows received by the savings depository.

Given the possibilities of cash-flow or reversion, and present or future values, the six combinations of these factors are:

the Future Value of Reversion (FVR) | - “Amount of 1” (Compound Interest) |

the Present Value of a Reversion (PVR) | - “Present Value of one” (Reversion) |

the Future Value of a Cash Flow (FVCF) | - “Amount of 1 per period” (Compounded) |

the Present Value of a Cash Flow (PVCF) | - “Present worth of an income stream” |

The Cash Flow of a Future Value (CFFV) | - “Sinking fund factor” |

The Cash Flow of a Present Value (CFPV) | - “Mortgage Constant” |

**SOURCE:**

“FINANCIAL ANALYSIS OF REAL ESTATE INVESTMENTS”

BY PROFESSOR MICHEAL J.CREAN (UNIVERSITY OF DENVER)